Abstract
The beam theory for a straight uniform bar of narrow rectangular cross section is discussed by using the orthotropic elastic plate (Scheibe) theory and Airy's stress functions in this paper. The Bernoulli-Euler hypothesis in the elementary beam theory is corresponding to the following assumptions of elastic moduli in the orthotropic elastic plate theory. Namely, the transverse shear elastic modulus is infinity as well as the transverse normal elastic modulus, and Poisson's ratios are zero. In a similar way, an equivalent beam theory including the effect of transverse shear deformation and warping can be obtained. On the other hand, Heki presented an analytical solution of the cantilever by using the theory of orthotropic plate (Scheibe). This analytical method is different from the proposed method. Therefore, in this paper a detailed comparison of the accuracy and mechanical property is made through calculation of the cantilever.
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